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Math Help - Help with series

  1. #1
    Newbie
    Joined
    Jul 2013
    From
    New Delhi
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    Help with series

    Hello everyone, I'm kind of new here so wasn't sure where to post a series problem.

    How would one go about summing

    \displaystyle \sum_{i=0}^{\infty} \frac{1}{(3i)!}

    I've tried to find similarities between it and the taylor series of hyperbolic cosine, but it isn't really working. I've tried repeated integration to derive a result with the factorial in the denominator but again, I get a non-convergent integral. Any help would be appreciated, thank you.
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  2. #2
    Super Member
    Joined
    Dec 2012
    From
    Athens, OH, USA
    Posts
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    Re: Help with series

    Hi,
    Your problem has a straight forward solution, but the details require some computation. The attachment shows how to solve the problem, but I left the algebraic details to you:

    Help with series-mhfcalc13.png
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